1. Field
Embodiments of the present invention generally relate to photonic crystals, and in particular the strain tuning of flexible photonic crystals
2. Description of the Related Art
Photonic crystals (PCs) are a class of materials that possess periodic dielectric constants. Such periodicity in dielectric constant strongly modulates the propagation of electromagnetic waves. There is a strong analogy between photonic crystals and real crystals. PCs exhibit photonic bands in a similar manner that electronic energy bands are formed in real crystals. Certain photonic crystals show photonic bandgaps, which are ranges of wavelengths in which generation and propagation of light is completely prohibited. Furthermore, the properties of PCs are likewise governed by the Bloch-Floquet theorem. Much like electronic dopants, defects may be introduced into PCs so that the periodicity in dielectric constants is perturbed locally. Such defects or impurities can act as active optical elements such as mirrors, waveguides and micro-cavities.
A photonic band gap provides a mechanism to confine light in a very small length scale. PC waveguides are typically created from semiconductor materials using e-beam lithography and standard semiconductor etching tools. To form a waveguide, a line defect is introduced to an otherwise periodic lattice, and light can be confined to the defect region and guided along the length of the waveguide. Those skilled in the art use well known analytical and numerical tools to design waveguides whose defect geometry is tailored towards certain wavelengths of light and different applications.
PCs can be used to build cavities with extremely high confinement factors in which strong enhancement of light-matter interaction occurs. Such high Q cavities exhibit strongly enhanced spontaneous emission rate and thus are ideal platforms to develop extremely low threshold lasers. Progress in nanofabrication techniques has made it possible to produce the complex PC structures required to build PC-based micro-cavities. The PC-based micro-cavity is typically defined by introducing a defect in an otherwise perfect PC structure. The defect acts as an optical cavity as it introduces a highly localized mode within the photonic bandgap.
PCs also exhibit extraordinary refraction and dispersion characteristics, orders of magnitude greater than in conventional optical materials. It has been shown that a beam entering the crystal with a small incident angle can experience strong positive or negative refraction with an extraordinarily large refraction angle. It should be noted that these properties are based on anisotropic and nonlinear dispersion and therefore do not require the existence of photonic bandgaps, significantly relieving material requirements. These novel properties present possibilities of achieving a new range of nanoscale optical devices that can focus, disperse, switch and steer light.
Recent developments have clearly demonstrated how PCs can generate, manipulate, process, transmit and detect light. There is significant promise in the possibility that PCs will be used extensively in compact and highly integrated nanoscale structures. These devices may provide the breakthroughs needed for the next-generation photonics technology. However, although many novel device schemes have been developed by extensive theoretical and experimental works, most of them are based on “passive” PC structures designed to perform certain functions without any means of external control.
A crucial innovation needed to fully exploit the unique optical properties of PCs is the ability to dynamically control or tune the photonic band structure and consequently their optical properties. There have been some efforts to achieve tunability by using electro-optic materials which change their refractive indices in response to an external electric field. Such research has predicted the tunability of photonic band structure by infiltrating liquid crystal (LC) into an opal structure. This work was soon followed by experimental demonstration of temperature tuning of photonic bandgap (PBG) in LC infiltrated PC structures. More recently, two-dimensional (2D) modeling studies showed tunability of the super-prism effect in 2D PCs infiltrated by LC and lead lanthanum zirconium titanate (PbLaZrTiO3, PLZT). However, a more rigorous 3D simulation taking explicitly into account the finite thickness of the slab PC structure predicted that tunability is limited due to the small attainable changes in the refractive index of LC. There have also been recent efforts at strain tuning of PCs. While all of these developments are encouraging, it is clear that there exist certain fundamental limitations on achievable tunability. For LCs, the attainable change in refractive index is typically on the order of 15% and, for PLZT, it is typically smaller. To maximize their promise, there is a clear need for wider tunability in PCs.
Information relevant to attempts to address these problems can be found at
U.S. Publication Numbers:US 2004/0076362US 2004/0170352International Publication Number:WO 02/10843WO 2004/008230WO 2004/008231Additional Publications:    S. Kim and V. Gopalan, “Strain-tunable photonic band gap crystals,” App. Phys. Lett. 78, 3015 (2001).    N. Malkova, S. Kim, and V. Gopalan, “Strain-tunable light transmission through a 90° bend waveguide in a two-dimensional photonic crystal,” App. Phys. Lett., 83, 1509 (2003).    N. Malkova, V. Gopalan, “Strain-tunable optical valves at T-junction waveguides in photonic crystals,” Phys. Rev. B, 68, 245115-1-6 (2003).    C. W. Wong, P. Rakich, S. Johnson, M. Qi, H. Smith, E. Ippen, L. Kimerling, Y. Jeon, G. Barbastathis, S.-G. Kim, “Strain-tunable silicon photonic band gap microcavities in optical waveguides” App. Phys. Lett. 84, 1242 (2004).    Y. B. Jeon, C. W. Wong, S. G. Kim, “Strain-Tuning of Nano-Optical Devices: Tunable Gratings and Photonic Crystals,” 12th International Conference on Solid-State Sensors, Actuators and Microsystems. Digest of Technical Papers, 202 (2003).    S. Jun and Y. Cho, “Deformation-induced bandgap tuning of 2D silicon-based photonic crystals,” Opt. Express 11, 2769 (2003).    S.-G. Kim, C. W. Wong, Y. B. Jeon, “Strain-tuning of Optical Devices with Nanometer Resolution”, Annals of CIRP 52, 2003.    N. Malkova, “Tunable resonant light propagation through 90° bend waveguide based on strained photonic crystal,” J. Phys.: Condens. Matter 16, 1523 (2004)    K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum”, Phys. Rev. Lett. 83, 967, (1999).    K. Yoshino, Y. Shinoda, Y. Kawagishi, K. Nakayama and M. Ozaki, “Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,” Appl. Phys. Lett. 75, 932, (1999).    S. W. Leonard, J. P. Mondia, H. M. van Driel, O. Toader, S. John, K. Busch, A. Birmer, U. Gosele and V. Lehmann, “Tunable two-dimensional photonic crystals using liquid-crystal infiltration,” Phys. Rev. B 61, R2389, (2000).    D. Scrymgeour, N. Malkova, S. Kim and V. Gopalan, “Electro-optic control of the superprism effect in photonic crystals,” Appl. Phys. Lett. 82, 3176 (2003).    S. Xiong and H. Fukshima, “Analysis of light propagation in index-tunable photonic crystals,” J. Appl. Phys. 94, 1286, (2003).    W. Park and C. J. Summers, “Optical Properties of Superlattice Photonic Crystal Waveguides”, Appl. Phys. Lett. 84, 2013 (2004).    S.-Y. Lin, V. M. Hietala, L. Wang and E. D. Jones, “Highly dispersive photonic band-gap prism,” Opt. Lett. 21, 1771 (1996).    H. Kosaka, T. Kawashima, A. Tomina, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, “Superprism phenomena in photonic crystals”, Phys. Rev. B 58, 10096 (1998).    W. Park and C. J. Summers, “Extraordinary Refraction and Dispersion in 2D Photonic Crystal Slabs”, Opt. Lett. 27, 1397 (2002).    L. Wu, M. Mazilu and T. F. Krauss, “Beam Steering in Planar-Photonic Crystals: From Superprism to Supercollimator,” J. Lightwave Technol. 21, 561 (2003).    S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis,” Opt. Express 8, 173 (2001).However, each one of the cited references suffers from at least one of the following disadvantages: limited tunability, limited functionality, fabrication difficulties, or excessive cost or size.
For the foregoing reasons, there is a need for widely tunable PCs that can be fabricated on a very small scale using largely conventional lithography techniques.